Changing every object in a group
you can do this with a script :


set the group name
select the chosen object and run the script


Note : you can choose to make them linked or non-linked duplicates

import bpy

group_name = 'Group'
linked = False   

chosen = bpy.context.object
mygroup = bpy.data.groups[group_name].objects 
for obj in mygroup:
    if linked :
        obj.data = chosen.data        # linked duplicates
    else :
        obj.data = chosen.data.copy() # Non linked duplicates